(CNN) -- Basketball star Dennis Rodman defended his controversial visit to North Korea with a team of former NBA players in a combative exchange Tuesday, saying it was a "great idea for the world."

In an exclusive interview with Chris Cuomo of CNN's "New Day," Rodman reacted angrily when pressed on whether the group should have traveled there given recent events in the secretive country.

The trip takes place just weeks after North Korea shocked the world by announcing the purge and execution of Kim's once-powerful uncle. There are also concerns for the welfare of U.S. citizen Kenneth Bae, who's been detained there for more than a year for reasons that are unclear.

The other former NBA players are due to take part in a controversial basketball game on the birthday of Kim Jong Un, the country's young, unpredictable leader. The friendly contest with North Korea's team is planned for Wednesday, when Kim is believed to turn 31.

Asked if he would take the opportunity to ask North Korean leaders about Bae, Rodman suggested the Korean-American had done something wrong but did not say what that was.

Growing angry with Cuomo and jabbing his finger toward the camera for emphasis, Rodman said, "Kenneth Bae did one thing. ... If you understand what Kenneth Bae did. Do you understand what he did in this country? No, no, no, you tell me, you tell me. Why is he held captive here in this country, why? ... I would love to speak on this.

"You know, you've got 10 guys here, 10 guys here, they've left their families, they've left their damn families, to help this country, as in a sports venture. That's 10 guys, all these guys here, do anyone understand that? Christmas, New Year's. ...

"I don't give a rat's ass what the hell you think. I'm saying to you, look at these guys here, look at them ... they dared to do one thing, they came here."

Bae, a married father of three, was arrested in November 2012 and sentenced in May to 15 years of hard labor. The North Korean government has said he was found guilty of "hostile acts" and attempts to topple the government.

He's suffered a series of health problems in detention, but pleas for his release have had no effect.

His mother, Myunghee Bae, who was allowed to visit in October, told CNN that her son was a devout Christian who had not understood the system in North Korea. North Korea is officially an atheist state and has punished missionaries in the past.

The White House reacts

At the White House, which has called for North Korea to release Bae, spokesman Jay Carney said Rodman is on a private trip "and our views about Kenneth Bae have not changed."

"I did not see some of the comments that Mr. Rodman made, but I am not going to dignify that outburst with a response," Carney said. "I am simply going to say that we remain gravely concerned about Kenneth Bae's health and continue to urge the DPRK authorities to grant his amnesty and immediate release on humanitarian grounds."After Rodman's outburst, fellow player Charles D. Smith tried to calm the discussion, but Rodman carried on, becoming increasingly agitated.

"Ain't no shill ... let me do this," he said to Smith, shaking Smith's hand off his arm. Addressing Cuomo, he continued, "Really? Really? I want to tell you one thing. People round the world, around the world, I want to do one thing.

"You're the guy behind the mic right now. We're the guys here doing one thing. We have to go back to America and take the abuse. Do you have to take the abuse that we're going to take? Do you, sir, are you going to take the abuse?

"One day, one day, this door is going to open because these 10 guys here, all of us, Christie, Vin, Dennis, Charles ... I mean everybody here, if we could open the door just a little bit for people to come here and do one thing."

Some of the players visible in the shot behind Rodman looked increasingly uncomfortable as he challenged the CNN anchor.

Smith pointed out that the basketball players made up only a part of a group of about 50 people visiting North Korea, with other Americans among them.

'He's got a great heart'

Smith also sought to defend Rodman, saying the visit was about basketball, not politics.

The players were invited by North Korea, Smith said, and are there as a kind of "cultural exchange" and to "put smiles on people's faces," not to influence the country's leaders.

"We've been doing these games for 3½ years," he said. "Outside of what people know of Dennis, you don't know Dennis. He's got a great heart, his passion is about children and families, that's why we are here.

"We are here because it's about doing great will around the world."

Smith outlined the charity projects he has been involved in worldwide through his sport, including visiting typhoon victims in Asia.

"We're doing what we do, we play basketball and that's what we love to do," Smith said.

"We didn't know it was going to take this kind of negative spin with what we are doing because we're not politicians, we're not ambassadors. We're here to do what we've been doing most of our lives."

Smith apologized for "the storm that has been created by our presence."

He also suggested that Rodman's use of the word "friend" for Kim should not be taken at face value.

Darren Prince, Rodman's agent for 16 years, told CNN on Sunday that Kenny Anderson, Cliff Robinson, Vin Baker, Craig Hodges, Doug Christie, and Smith would play against the North Korean senior national team.

The current trip is Rodman's fourth to the isolated nation, part of a project he has described as "basketball diplomacy."

But the U.S. State Department says that it has nothing to do with Rodman's visits to North Korea and that attention should be focused on the brutality of Kim's regime.

The NBA also distanced itself Tuesday from Rodman.

"The NBA is not involved with Mr. Rodman's North Korea trip and would not participate or support such a venture without the approval of the U.S. State Department," NBA Commissioner David Stern said in a statement released by the league.

"Although sports in many instances can be helpful in bridging cultural divides, this is not one of them."

'Friend for life'

Rodman, 52, struck up an unlikely friendship with Kim when he traveled to North Korea for the first time in February, bringing a team of Harlem Globetrotters for an exhibition game watched by Kim, who is a basketball fan.

Kim later met and dined with the flamboyant basketball star, and Rodman told his host he had "a friend for life," shrugging off international condemnation of the country's human rights record.

However, on his last trip -- which took place last month less than a week after North Korea announced the execution of Kim's uncle and top aide, Jang Song Thaek -- Rodman didn't get to meet Kim.

The international outcry over the killing of Jang prompted Paddy Power, the online betting company that had supported Rodman's project, to withdraw its association with the event.

But Rodman has pressed on with the plan. He met and coached the North Korean team on his previous trip last month.